xxx I need a public ip
I must tell the app to connect to the ip
That's all done by the Fritzbox when you set up a Wireguard tunnel. Your current IP will always be refreshed via MyFritz, you don't have anything to do with that.
I already used this setup before I got a public IP.
xxx I can use a vpn like mullvad to connect?
No, as Mullvad isn't a direct VPN connection from a device to your Fritzbox/router. You could set up Mullvad or other VPNs directly on your Fritzbox for WAN, then your whole home network is protected and single devices you could connect to the Fritzbox via Wireguard, so these devices respectively the tunneled apps are protected too, but you will get a connection speed loss for the tunneled apps, depending on upload speed of your home internet connection.